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Correlation
Point-Biserial Correlation — Binary × Continuous
Express a two-group comparison as a correlation between a 0/1 group code and a continuous outcome. Shows the exact mathematical equivalence to the independent t-test.
📊 r_pb(10) = .904, p < .001
Step-by-step solution
🔗 34 · Point-Biserial Correlation — Binary × Continuous
Treatment Group and Outcome Score — the Correlation View of a t-test
Correlation
Research Question:
12 participants were split into a Control group and a Treatment group (n=6 each). Instead of running an independent t-test, we can express the same relationship as a correlation between group membership (0/1) and outcome score.
| Participant | Group (0=Control, 1=Treatment) | Score |
|---|---|---|
| 1 | 0 | 72 |
| 2 | 0 | 68 |
| 3 | 0 | 75 |
| 4 | 0 | 70 |
| 5 | 0 | 74 |
| 6 | 0 | 69 |
| 7 | 1 | 82 |
| 8 | 1 | 88 |
| 9 | 1 | 79 |
| 10 | 1 | 85 |
| 11 | 1 | 90 |
| 12 | 1 | 84 |
Point-biserial r is just Pearson's r applied to a 0/1 group code
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1Group means:
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2Compute Pearson's r between the 0/1 group code and score, exactly as with any two continuous variables:
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3Significance test:
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4Teaching point — this is the same test as the independent t-test: This t and df are identical to what an independent-samples t-test on Control vs. Treatment would give — point-biserial r is mathematically the correlation-equivalent view of the same comparison, not a separate result.
.904
r_pb
6.704
t(10)
<.001
p
.818
r²_pb
🔴 Significant — r_pb(10) = .904, p < .001. Treatment-group membership is strongly associated with higher scores.
APA-7
A point-biserial correlation revealed a strong positive association between treatment-group membership and outcome score, r_pb(10) = .904, p < .001, with the treatment group (M = 84.67) scoring markedly higher than the control group (M = 71.33).